Stats Ch. 5 (exam three)
When raw scores are transformed to z-scores, their average deviation is what?
1
the standard deviation of any z-distribution is ________
1
With a sample mean of 50, and a standard deviation of 10: 1. What is z for X = 44? 2. What X produces z = -1.3
1. -.60 2. 37
All normal z-distributions share three important characteristics, they are:
1. A z-distribution always has the same shape as the raw score distribution - so if underlying raw score distrib. is normal, z-distrib. is normal too 2. the mean of any z-distribution is 0 - whatever mean of raw scores is, always transforms to 0 3. the standard deviation of any z-distribution is 1 - avg. deviation is now 1 for z-distrib.
a z-score always has 2 components, what are they?
1. a positive or negative sign indicating if the score is above or below the mean 2. the absolute value of the z-score (ignoring the sign) which indicates how FAR the score is from the mean in standard deviations
What three things does the central limit theorem communicate about sampling distributions?
1. a sampling distribution is always an approximately normal distribution 2. the mean of the sampling distribution equals the mean of the underlying raw score population used to create the sampling distribution 3. the standard deviation of the sampling distribution is mathematically related to the standard deviation of the raw score population
What three things do z-scores do?
1. they describe relative standing 2. they compare scores of different distributions 3. they compute the relative frequency of scores
What is the difference between a z-distribution and the sampling distribution of means?
A z distribution is a standardization of the distribution of a set of raw data. A sampling distribution of means is a hypothetical distribution (though it is technically a z -distribution) that we create by taking an infinite number of samples from a population and plotting the probability of getting that sample mean on the z distribution
Why are z-scores called standard scores?
Because z-scores use relative standing to equate scores from different variables or distributions so we have a standard way to compare them.
What are the steps for finding the relative frequency of sample means above or below a specified mean?
Compute the standard error of the mean, transform the sample mean into a z-score, and use the z-table to determine the proportion of the curve above or below the mean. This proportion is the expected relative frequency of the corresponding means.
How do we use a sampling distribution of means?
It is a model of all sample means to which we can compare our sample mean.
When using a sampling distribution of means, what do we mean by "underlying raw score population?"
It is the raw score population used to create a particular sampling distribution.
What is the standard error of the mean and what does it indicate?
It is the standard deviation of the sampling distribution of means, indicating the "average" deviation of sample means from the μ of the sampling distribution.
What is a sampling distribution of means?
It shows all possible sample means that occur when a particular raw score population is infinitely sampled using a particular
Kathy made a score of 75 on her biology exam. Shara made a score of 65 on her chemistry exam. Kathy insists that she did better than Shara (overall). A) Can Kathy make this assumption? B) Why or why not?
No, because you can't compare two separate distributions on equal terms. To interpret the meaning of these scores, we need a frame of reference to show how well Kathy and Shara did compared to other deviations in their classes. She must put these two scores on the same scale
What two factors determine the size of a z-score?
The size of the score's deviation and the size of the standard deviation.
A + z indicates the score is _______ the mean, a - z indicates the score is ________ the mean
above, below
negative z-scores become increasingly larger as we look to the _______ of the distribution, and these scores occur _______ frequently
become increasingly larger as we look to the left of the distribution, and these scores occur less frequently
Positive z-scores become increasingly larger as we look to the _______ of the distribution, and these scores occur ________ frequently
become increasingly larger as we look to the right of the distribution, and occur less frequently
How do we transform a raw score from a sample into a z-score?
by first subtracting the mean from the raw score and then dividing by the standard deviation
How do we transform an already known z-score to a raw score?
by multiplying the z-score times the standard deviation, and then adding the mean
a statistical principle that defines the mean, standard deviation, and shape of a sampling distribution
central limit theorem
the statistical principle called the _________ defines the shape, the mean, and the standard deviation of a sampling distribution
central limit theorem
the absolute value of the z indicates the scores __________ from the mean
distance
T or F: the mean of all z-distributions is equal to 1
false; the mean of all z-distributions is equal to ZERO
the standard normal curve is best used with what kind of data?
if 1. we have a large population or sample 2. the scores or interval or ratio 3. the scores are normally distributed
what is the importance of the central limit theorem?
it allows us to describe a sampling distribution without having to infinitely sample a population of raw scores
when computing a percentile, we add .50 to the proportion obtained from the z-table when the z-score has a _______ sign, but not when the z-score has a ______ sign
positive, negative
reflects the systematic evaluation of the score by comparing it to the sample or population in which the score occurs
relative standing
when we evaluate a raw score relative together scores in the data, we are describing the scores _______
relative standing
a frequency distribution showing all possible sample means that occur when samples of a particular size are drawn from a population
sampling distribution of means
A z-score indicates how far a score is from the mean when measured in what?
standard deviations
the standard deviation of the sampling distribution is called the ________
standard error of the mean
the standard deviation of the sampling distribution of means
standard error of the mean
To determine the relative frequency of raw scores, transform them into z-scores and then use the _____________
standard normal curve
a perfect normal curve that serves as a model of any approximately normal z-distribution
standard normal curve
z-scores are often referred to as what?
standard scores
If a score has a z-score of 0, what does this mean?
that the score is EQUAL TO the mean and is in the CENTER
what does a z-score indicate?
the distance a score is above or below the mean when measured in standard deviation units
Our first calculation when attempting to transform raw scores to z-scores is what?
the scores deviation, or how far a score is from the mean (X - sample mean)
we always refer to the population of raw scores used to create the sampling distribution as what?
the underlying raw score population
T or F: although scores may have different distributions, the location of each z-score is the same
true
T or F: you cannot compare two different distributions if they are not on the same scale
true
T or F: the z-distribution will always have the same shape as the raw score distribution
true; if the raw-score distribution shape is normal, the z-score distribution shape will be normal too
T or F: All z-distributions are laid out in the same way
true; this allows for z-scores to form a standard way to communicate relative standing
the mean of the sampling distribution always equals the mean of the _________ population
underlying raw score
the symbol for a z-score is
z
the distribution produced by transforming all raw scores in a distribution into z-scores
z-distribution
statistic that indicates the distance a score is fro its mean when measured in standard deviation units
z-score
to compare raw scores from two different variables, transform the scores into ________
z-scores
what are the 3 major uses of z-scores with individual's scores?
z-scores are used to determine 1. relative standing 2. compare scores from different variables 3. compute relative frequency and percentile
the mean of any z-distribution is _______
zero